Finite Group Databasebeta

← C3×#3482 #87366

Subgroups — C3×#3482 #87366

Order 384.

1094 conjugacy classes of subgroups.

The subgroup lattice has 256 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#557C211yesmaximal, characteristic, complemented
2C3×#556C213yesmaximal, complemented
3C3×#552C216yesmaximal, complemented
4C3×D4×Q8C211yesmaximal, characteristic, complemented
5C3×#548C212yesmaximal, complemented
6C3×#547C213yesmaximal, complemented
7C3×#533C213yesmaximal, complemented
8C3×#529C216yesmaximal, complemented
9C3×C4×#41C213yesmaximal, complemented
10C3×C4×#41C211yesmaximal, characteristic, complemented
11C2×C3×C4×Q8C212yesmaximal, complemented
12#3482C311yesmaximal, characteristic, direct product factor, Sylow
13C2×C3×#41C2213yes—
14C2×C3×#41C2211yescharacteristic
15C22×C3×Q8C2212yes—
16C3×C4⋊Q8C2213yes—
17C3×C4⋊Q8C2213yes—
18C3×#126C22112yes—
19C3×#125C2216yes—
20C3×#125C2216yes—
21C3×#124C2216yes—
22C3×#123C22112yes—
23C3×C22⋊Q8C2216yes—
24C3×C22⋊Q8C2216yes—
25C3×C22⋊Q8C2216yes—
26C3×#121C2216yes—
27C3×C4×Q8C2211yescharacteristic
28C3×C4×Q8C2216yes—
29C3×C4×Q8C2212yes—
30C3×C4×Q8C2216yes—
31C3×C4×Q8C2213yes—
32C3×C4×Q8C2211yescharacteristic
33C3×C4×Q8C2213yes—
34C3×C4×D4C2211yescharacteristic
35C3×C4×D4C2213yes—
36C3×C4×D4C2216yes—
37C3×C4×D4C2213yes—
38C3×C4×D4C2213yes—
39C3×C4×D4C2216yes—
40C3×#117C2213yes—
41C3×#117C2216yes—
42C3×#117C2213yes—
43C3×#117C2216yes—
44C2×C3×C4⋊C4C2216yes—
45C2×C3×C42C2216yes—
46C2×C3×C42C2213yes—
47#557C2×C311yescharacteristic, complemented
48#556C2×C313yescomplemented
49#552C2×C316yescomplemented
50D4×Q8C2×C311yescharacteristic, complemented
51#548C2×C312yescomplemented
52#547C2×C313yescomplemented
53#533C2×C313yescomplemented
54#529C2×C316yescomplemented
55C4×#41C2×C313yescomplemented
56C4×#41C2×C311yescharacteristic, complemented
57C2×C4×Q8C2×C312yescomplemented
58C3×#41—24no—
59C3×#41—212no—
60C2×C3×Q8—28no—
61C2×C3×Q8C2316yes—
62C2×C3×Q8C2313yes—
63C2×C3×Q8C2311yescharacteristic
64C2×C3×D4C2316yes—
65C2×C3×D4C2313yes—
66C2×C3×D4C2311yescharacteristic
67C22×C3×C4C2316yes—
68C22×C3×C4C2316yes—
69C22×C3×C4C2313yes—
70C22×C3×C4C2313yes—
71C22×C3×C4C2312yes—
72C22×C3×C4C2313yes—
73C3×C4⋊C4C2313yes—
74C3×C4⋊C4C2316yes—
75C3×C4⋊C4C23112yes—
76C3×C4⋊C4C2311yescharacteristic
77C3×C4⋊C4C2316yes—
78C3×C4⋊C4C2313yes—
79C3×C4⋊C4C2313yes—
80C3×C4⋊C4C2316yes—
81C3×C4⋊C4C2316yes—
82C3×C4⋊C4C2316yes—
83C3×C22⋊C4C2312yes—
84C3×C22⋊C4C2316yes—
85C3×C22⋊C4C2316yes—
86C3×C22⋊C4C2316yes—
87C3×C22⋊C4C23112yes—
88C3×C42C2313yes—
89C3×C42C2316yes—
90C3×C42C2313yes—
91C3×C42C2316yes—
92C3×C42C2313yes—
93C3×C42C2311yescharacteristic
94C3×C42C2316yes—
95C2×#41C22×C313yes—
96C2×#41C22×C311yescharacteristic
97C22×Q8C22×C312yes—
98C4⋊Q8C22×C313yes—
99C4⋊Q8C22×C313yes—
100#126C22×C3112yes—
101#125C22×C316yes—
102#125C22×C316yes—
103#124C22×C316yes—
104#123C22×C3112yes—
105C22⋊Q8C22×C316yes—
106C22⋊Q8C22×C316yes—
107C22⋊Q8C22×C316yes—
108#121C22×C316yes—
109C4×Q8C22×C311yescharacteristic
110C4×Q8C22×C316yes—
111C4×Q8C22×C312yes—
112C4×Q8C22×C316yes—
113C4×Q8C22×C313yes—
114C4×Q8C22×C311yescharacteristic
115C4×Q8C22×C313yes—
116C4×D4C22×C311yescharacteristic
117C4×D4C22×C313yes—
118C4×D4C22×C316yes—
119C4×D4C22×C313yes—
120C4×D4C22×C313yes—
121C4×D4C22×C316yes—
122#117C22×C313yes—
123#117C22×C316yes—
124#117C22×C313yes—
125#117C22×C316yes—
126C2×C4⋊C4C22×C316yes—
127C2×C42C22×C316yes—
128C2×C42C22×C313yes—
129C23×C3C2413yes—
130C23×C3C2412yes—
131C3×Q8—212no—
132C3×Q8—26no—
133C3×Q8#4114yescomplemented
134C3×D4—212no—
135C3×D4—26no—
136C3×D4#4114yescomplemented
137C2×C3×C4—212no—
138C2×C3×C4—212no—
139C2×C3×C4—26no—
140C2×C3×C4—26no—
141C2×C3×C4—24no—
142C2×C3×C4—26no—
143C2×C3×C4C2412yes—
144C2×C3×C4C2411yescharacteristic
145C2×C3×C4C2413yes—
146C2×C3×C4C2413yes—
147C2×C3×C4C2416yes—
148C2×C3×C4C2416yes—
149C2×C3×C4C2413yes—
150C2×C3×C4C2411yescharacteristic
151C2×C3×C4C2411yescharacteristic
152#41—24no—
153#41—212no—
154C2×Q8—28no—
155C2×Q8C23×C316yes—
156C2×Q8C23×C313yes—
157C2×Q8C23×C311yescharacteristic
158C2×D4C23×C316yes—
159C2×D4C23×C313yes—
160C2×D4C23×C311yescharacteristic
161C22×C4C23×C312yes—
162C22×C4C23×C316yes—
163C22×C4C23×C316yes—
164C22×C4C23×C313yes—
165C22×C4C23×C313yes—
166C22×C4C23×C313yes—
167C4⋊C4C23×C313yes—
168C4⋊C4C23×C316yes—
169C4⋊C4C23×C3112yes—
170C4⋊C4C23×C311yescharacteristic
171C4⋊C4C23×C316yes—
172C4⋊C4C23×C313yes—
173C4⋊C4C23×C313yes—
174C4⋊C4C23×C316yes—
175C4⋊C4C23×C316yes—
176C4⋊C4C23×C316yes—
177C22⋊C4C23×C312yes—
178C22⋊C4C23×C316yes—
179C22⋊C4C23×C316yes—
180C22⋊C4C23×C316yes—
181C22⋊C4C23×C3112yes—
182C42C23×C313yes—
183C42C23×C311yescharacteristic
184C42C23×C313yes—
185C42C23×C316yes—
186C42C23×C316yes—
187C42C23×C313yes—
188C42C23×C316yes—
189C22×C3—22no—
190C22×C3—22no—
191C22×C3—23no—
192C22×C3—23no—
193C22×C3—23no—
194C22×C3C2×#4114yes—
195C22×C3C2511yescharacteristic
196C3×C4—23no—
197C3×C4—21no—
198C3×C4—26no—
199C3×C4—26no—
200C3×C4—22no—
201C3×C4—23no—
202C3×C4C2×#4116yes—
203C3×C4C2×#4112yes—
204C3×C42−1+412yes—
205C23C24×C313yes—
206C23C24×C312yes—
207Q8—212no—
208Q8—26no—
209Q8C3×#4114yescomplemented
210D4—212no—
211D4—26no—
212D4C3×#4114yescomplemented
213C2×C4—212no—
214C2×C4—212no—
215C2×C4—26no—
216C2×C4—26no—
217C2×C4—24no—
218C2×C4—26no—
219C2×C4C24×C312yes—
220C2×C4C24×C311yescharacteristic
221C2×C4C24×C313yes—
222C2×C4C24×C313yes—
223C2×C4C24×C316yes—
224C2×C4C24×C316yes—
225C2×C4C24×C313yes—
226C2×C4C24×C311yescharacteristic
227C2×C4C24×C311yescharacteristic
228C2×C3—24no—
229C2×C3—43no—
230C2×C3C22×#4111yescharacteristic
231C2×C3C22×#4111yescharacteristic
232C2×C3C2×2−1+411yescharacteristic
233C22—22no—
234C22—22no—
235C22—23no—
236C22—23no—
237C22—23no—
238C22C2×C3×#4114yes—
239C22C25×C311yescharacteristic
240C4—23no—
241C4—21no—
242C4—26no—
243C4—26no—
244C4—22no—
245C4—23no—
246C4C2×C3×#4116yes—
247C4C2×C3×#4112yes—
248C4C3×2−1+412yes—
249C3#348211yescharacteristic, direct product factor, Sylow
250C2—24no—
251C2—43no—
252C2C22×C3×#4111yescharacteristic
253C2C22×C3×#4111yescharacteristic
254C2C2×C3×2−1+411yescharacteristic
subgroupG/H
centerC2×C3×C4C24
commutator, Frattini, cosocleC22C25×C3
socleC22×C3C25
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C2×C3×C4 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C3×#557C2semidirect
2. C3×#556C2semidirect
3. C3×#552C2semidirect
4. C3×D4×Q8C2semidirect
5. C3×#548C2semidirect
6. C3×#547C2semidirect
7. C3×#533C2semidirect
8. C3×#529C2semidirect
9. C3×C4×#41C2semidirect
10. C3×C4×#41C2semidirect
11. C2×C3×C4×Q8C2semidirect
12. #3482C3direct (N × H)
47. #557C2×C3semidirect
48. #556C2×C3semidirect
49. #552C2×C3semidirect
50. D4×Q8C2×C3semidirect
51. #548C2×C3semidirect
52. #547C2×C3semidirect
53. #533C2×C3semidirect
54. #529C2×C3semidirect
55. C4×#41C2×C3semidirect
56. C4×#41C2×C3semidirect
57. C2×C4×Q8C2×C3semidirect
133. C3×Q8#41semidirect
136. C3×D4#41semidirect
209. Q8C3×#41semidirect
212. D4C3×#41semidirect
249. C3#3482direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C3×#5572
C3×#5562
C3×#5522
C3×D4×Q82
C3×#5482
C3×#5472
C3×#5332
C3×#5292
C3×C4×#412
C2×C3×C4×Q82
#34823